has been modelled by nag_estimate_agarchI (g13fac) and the estimated conditional variances and residuals are contained in the arrays ht and et respectively. Then nag_forecast_agarchI (g13fbc) will use the last maxp,q elements of the arrays ht and et to estimate the conditional variance forecasts, ht∣ψT, where t=T+1,…,T+τ and τ is the forecast horizon.

Engle R and Ng V (1993) Measuring and testing the impact of news on volatility Journal of Finance48 1749–1777

Hamilton J (1994) Time Series Analysis Princeton University Press

5 Arguments

1:
num – IntegerInput

On entry: the number of terms in the arrays ht and et from the modelled sequence.

Constraint:
maxp,q≤num.

2:
nt – IntegerInput

On entry: τ, the forecast horizon.

Constraint:
nt>0.

3:
p – IntegerInput

On entry: the GARCHp,q argument p.

Constraint:
0<maxp,q≤num, ​p≥0.

4:
q – IntegerInput

On entry: the GARCHp,q argument q.

Constraint:
0<maxp,q≤num, ​q≥1.

5:
theta[q+p+1] – const doubleInput

On entry: the first element must contain the coefficient αo and the next q elements must contain the coefficients αi, for i=1,2,…,q. The remaining p elements must contain the coefficients βj, for j=1,2,…,p.